Guide to Graph Algorithms by K Erciyes

Author:K Erciyes
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Theorem 8.3

(Menger’s Theorem, edge version) Let be the maximum number of edge disjoint paths between the vertices u and v. A graph is k-edge-connected if and only if each vertex pair in the graph is connected by at least k edge-disjoint paths.

8.2.4 Connectivity in Digraphs

Connectivity in digraphs require further specifications as the connection between vertices is not symmetric in such graphs. That is, it may be possible to reach a vertex v from a vertex u but not vice versa. We require that there is a path between every pair of vertices in both directions in a digraph for the connectivity to hold. A strongly connected digraph is defined as follows.

Definition 8.12

(strongly connected digraph) A digraph is called strongly connected if for every pair of vertices, there is a path from u to v and a path from v to u.

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